Last season's scars still show on Sir Alex Ferguson. "No, no, no" he said when asked whether a 12-point advantage with 12 games to go has placed the Premier League title beyond Manchester City. The reply was surely one of professional courtesy. Privately he must know it. Old Trafford certainly did after a comfortable defeat of Everton. Manchester United are too ruthless, too consistent, to offer their neighbours hope now.

This fixture cost United a 20th league title last season, according to a manager who has vowed that late collapses – that saw Everton recover from 4-2 down with minutes remaining at Old Trafford and an eight-point lead dissolve over six matches – will not be repeated. United are following Ferguson's instruction and number 20 beckons after the return of David Moyes' team proved another significant step in the title race. Everton were dispatched in efficient fashion by a side blinkered from an impending date with Real Madrid in the Champions League.

Goals from Ryan Giggs, scoring for the 23rd season in a row for United, and Robin Van Persie, who offers another reason for Roberto Mancini to rue his rival's relentlessness, sealed victory before half-time as the league leaders capitalised on City's defeat at Southampton. The observing José Mourinho may have studied better Ferguson teams, more formidable European rivals, but United have a self-belief and potency that threatens his ambition of becoming the first man to win the European Cup with three different clubs.

City's defeat on the south coast was not the cue for United to ease up against Everton with Madrid in mind. In fact it was quite the opposite. Everything about the league leaders' approach was about getting the job done. From Ferguson's team selection – the opposite of the changed selection he proposed on Friday – to the home side's frenetic start, the determination to land a decisive victory was evident. Ferguson was not about to let another slip by the reigning champions to escape unpunished.

United dominated from the opening whistle, with Phil Jones' limpet-like marking of Marouane Fellaini underlining their refusal to allow Everton any time to settle on the ball. Fellaini had been instrumental in Everton's 4-4 draw here last season and victory at Goodison Park at the start of this campaign but he and his team-mates were hassled each time they touched the ball. "They man-marked Fellaini with Phil Jones and set out their stall to stop us doing what we wanted to do," said Moyes. "They played as if they meant it. They were not thinking about a midweek game, that's for sure. They were really competitive and we didn't compete enough."

The visitors were behind before they were able to find any rhythm. Van Persie should have opened the scoring with 10 minutes gone when Wayne Rooney was left unchallenged to pierce the Everton defence. Phil Neville's attempted offside trap malfunctioned, allowing Van Persie to round Tim Howard and bring Old Trafford to its feet in anticipation of his 23rd goal of the season. Astonishingly the Dutch striker struck the outside of the post with his weaker right foot. Neville would later repeat his error. Van Persie would not.

Everton's preparations had been disrupted by the late withdrawal of Sylvain Distin through illness. That meant an unexpected reprieve for John Heitinga, who was at fault for all three Aston Villa goals at Goodison last Saturday – his worst display in an Everton shirt, he later confessed – and West Bromwich Albion's consolation before that. The recall brought another costly mistake. Antonio Valencia outjumped Leighton Baines to Rafael's long ball and Heitinga completely misread the bounce to leave Van Persie goalside. The United forward had time to shoot but unselfishly squared to Giggs, who rolled the ball in off Howard's post with his right foot.

Giggs made his United debut against Everton on 2 March 1991, a moment captured in the match-day programme with a photograph of the precocious winger standing in front of Dave Watson. Here, almost 22 years later, the remarkable 39-year-old picked a fitting opponent against whom to score his first goal of the season and thus extend his scoring record for United.

Everton belatedly showed some belief and composure on the ball following Giggs's goal. Leon Osman forced David de Gea into his first save of the game with a volley from 20 yards and Nemanja Vidic made an important block from Kevin Mirallas as the visitors' Belgian contingent began to impose themselves. They rarely threatened an equaliser, however, and United added the cushion of a second goal on the stroke of half-time when Rafael sent Van Persie clear of Neville's offside appeal. Again the striker went round the Everton goalkeeper's left and this time, despite Heitinga's best efforts on the line, he finished convincingly.

Howard saved superbly from Jonny Evans in the second half and United, despite a late scare when Nikica Jelavic replaced the anonymous Victor Anichebe in Everton's attack, held their lead comfortably. As City fumble their hold on the Premier League trophy, United's grip tightens. It was a fitting way for United's players to mark the recent 55th anniversary of the Munich disaster. Before kick-off supporters had played their part on the Stretford End, raising a banner that showed the Busby Babes lining up before their final game in Belgrade and above the words "We'll Never Die".